Definite and indefinite articles when referring to generic abstract objects

My classmate wrote a text about zoos in general, and the word "zoos" in plural form is mentioned many times in it. Later in the text he uses singular form "zoo" two times with indefinite articles, and both times he still refers to an abstract zoo, not to specific one.

He wrote:

The place where animals can obtain shelter is a zoo.

You can take the kids to a zoo.

I'm having trouble in figuring out whether it is correct or not. I think that he should have used a definite article the second time, because he already mentioned a singular abstract zoo, but he argues that he refers to "two different singular abstract zoos".

So which article should be used in a second sentence?

Answer

Sadly, 'rules' that people devise to 'make article use simper' are almost always too broad-brush.

I'd prefer a more realistic first sentence:

A zoo is 'an establishment which maintains a collection of wild
animals, typically in a park or gardens, for study, conservation, or
display to the public'.

{ODO}

'You can take the kids to a zoo.'

then works because you're still referring to an abstract example.

'You can take your kids to the zoo.'

also works, but not because 'zoo' has already been mentioned in the first sentence here: it is equally acceptable to use the definite article in expressions like

'We're going to the seaside.'

'We went to the opera three times last year'

'We often go to the cinema'

where (1) this is the first mention of 'seaside', 'opera' etc

(2) the actual seaside resort / venue, opera house or cinema is not specified (and there may in fact be more than one involved). Note that 'You can take the kids ...' displays a usage somewhere between this usage and a specifying one (your kids).